How do you find on what time interval is the concentration of the drug increasing if suppose a certain drug is administered to a patient, with the percent of concentration in the bloodstream t hr later given by K(t)= 8t / (t^2 + 1)?

1 Answer
Noah G
Apr 15, 2018

The concentration is increasing on 0 ≤ t < 1

Explanation:

You will need to start by differentiating.

K'(t) = (8(t^2 + 1) - 8t(2t))/(t^2 + 1)^2

K'(t) = (8t^2 + 8 - 16t^2)/(t^2 + 1)^2

K'(t) = (8 - 8t^2)/(t^2 + 1)

This will have a critical number when K'(t) = 0.

0 = 8 - 8t^2

8t^2 = 8

t = +-1

But since t > 0, only t =1 is acceptable.

You will notice that whenever t > 1, the derivative turns negative, therefore the amount of drug in the patients system is increasing for the first hour, with 0 ≤ t < 1.

Hopefully this helps!

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